The present disclosure deals with wireless receivers including demodulators using signal analyzers, methods thereof, and applications of each. This disclosure deals more specifically with but not limited to such apparatus and methods employing short-time signal analysis including recursive structures and methods of such analysis.
Wireless receivers including demodulators using signal analyzers and signal analysis are known. That notwithstanding, practitioners in the field continue to devote extensive attention to the topic, perhaps due to it""s relative significance as nearly all electronic or other systems require some signal analysis. The general form and concept of short-time signal analysis, although more recently developed, is similarly known.
Short-time signal analysis is a tool especially suitable for adaptive estimation. Adaptive estimation estimates time varying features of non-stationary signals or systems by using a window to localize and weight data and then applying stationary estimation to the localized data to generate a local estimate or signal feature. Short time signal analysis is useful for various forms of adaptive signal processing, such as adaptive filtering, time/frequency analysis, time scale analysis, filter bank design, etc. Recursive short-time signal analysis is a method of implementing short-time signal analysis that relies on previous estimates of a local feature to estimate the local feature for a new time. Apparatus and methods suitable for accurate and efficient implementations of recursive short-time signal analysis are evidently very rare and yet highly desirable, especially for real time processing.
In a sampled signal context a mathematical expression for the weighting or localizing process over a sliding time frame of a sampled signal at sample time n may be written as: {overscore (d)}k(m|n)=wk(m)dk(nxe2x88x92m) where d(n) is a sample taken at n, w(m) is the localizing and weighting function often referred to as a window and the k subscript allows for different windows. One particular feature estimation procedure is known as the short time Fourier Transform that is defined in a sampled signal context as:             F      k        (          n      ❘              ω        k              )    =            ∑      m        ⁢          xe2x80x83        ⁢                  ⅇ                              -            j                    ⁢                      xe2x80x83                    ⁢          m          ⁢                      xe2x80x83                    ⁢                      ω            k                              ⁢                        w          k                ⁡                  (          m          )                    ⁢                                    d            k                    ⁡                      (                          n              -              m                        )                          ·            
For xcfx89k=0 this provides an average based estimation for all k and for xcfx89kxe2x89xa00 this provides a time-frequency estimate or frequency dependent energy or amplitude estimate at xcfx89k.
As a generality the specific characteristics of wk(m) determine the relative accuracy of the feature estimates obtained,. upon for example execution of the above equation, and additionally determine the relative efficiency or computational burden incurred in the implementation of a recursive structure suitable for obtaining the above estimations. Various windows or wk(m) have been proposed and evaluated but all have suffered from either poor accuracy or undue computational burden thus severely limiting the utilization of recursive short time signal analysis to those circumstances where either accuracy was unimportant or substantial computational resources were available. Clearly a need exists for efficient and accurate signal analyzers using short-time signal analysis and methods of doing so.